Dr. E. E. Escultura is a world-class mathematician with over fifty technical publications in renowned refereed international journals and conference proceedings. He graduated Ph. D. in mathematics from the University of Wisconsin. His advisor is the famous British mathematician, L. C. Young whose parents, W. H. and G. C. Young, were themselves famous mathematicians. He was a former Mathematics Professor at the University of the Philippines. Now, he is a Research Professor at Lakshmikantham Institute for Advanced Studies and at Departments of Mathematics and Physics, GVP College of Engineering, Jawaharlal Nehru Technical University, Kakinada Campus
Madurawada, Visakhapatnam, India.
"THE HYBRID GRAND UNIFIED THEORY by V Lakshmikantham (Florida Institute of Technology, USA), E Escultura (Lakshmikantham Institute for Advanced Studies, India), & S Leela (Florida Institute of Technology, USA). In this book, an attempt is made to provide a hybrid grand unified theory to understand the universe, both in its micro/quantum aspects as well as macro/galactic aspects. The book describes a truly hybrid theory as it encompasses both the modern and ancient theories of the universe, together with its functioning at all levels of human comprehension. One of its authors,
Dr Escultura, was nominated in 2005 for a Nobel Prize for his flux theory of gravitation. From then on this theory has been improved, clarified and is now known as the hybrid grand unified theory. This book deals with this new bold theory, unifying mathematics and physics, and answering some open fundamental questions and paradoxes in these disciplines. The book also describes what the ancient scientists knew about these matters."
https://www.worldscibooks.com/mathematics/l009.html
“Most recent is the case of Professor Eddie Escultura, from the Philippines, a great mathematical brain who contributed something novel in the field of quantum physics. He was considered for the Nobel this year by the committee only to be rejected in favour of Professor Glauber. But the developments following this would reveal the sickness that has afflicted the Nobel committee. Professor Gerholms, an eminent physicist on the Nobel committee resigned from the committee to protest the dropping of Eddie. He goes one step further. In a personal letter to Prof. Escultura, Prof Gerholms wrote as to what went on inside the committee room and named two prominent members of the committee lobbying for their candidates. Gerholms in his resignation letter wrote to the committee that lobbying is highly objectionable inside the Nobel committee. Bold man indeed!”
Here are the Abstracts and Summary of Publications on GUT, its Mathematics and Applications of Dr. Edgar E. Escultura
This series of publications are the basis of the Grand Unified Theory (GUT) and its much broader extension, Grand Unification of Natural Dynamics (GUND). GUND encompasses macro and quantum gravity and unites all physical systems from dark to visible and organic to inorganic.
(1) The Mathematics of Singularities. Trans. National Academy of Science and Technology (Philippines), Manila, 1992, pp. 141 - 153.
Abstract. This is the initial development of the generalized fractal that
provides the essential mathematics for the study of matter and its dark and
visible components. It shows how a curve of any length can be shrunk into
an infinitesimal neighborhood of a point with its length preserved, the
essence of black hole formation. The paper paves the way for the
development of the superstring as a physical concept and the basic
constituent of dark matter. Its axial projection is a rapid sinusoidal curve.
Shrinking it towards infinitesimal neighborhood enhances its frequency and
raises its latent energy indefinitely. A black hole is massive concentration of
non-agitated superstrings that accumulates in the eye of cosmological and
atomic vortices.
(2) Probabilistic Mathematics and Applications to Dynamic Systems Including Fermat's Last Theorem, Proc. 2nd International Conference on Dynamical Systems and Applications, Dynamic Publishers, Inc., Atlanta, 1996, pp. 147 - 152.
Abstract. The paper characterizes undecidability and establishes that
Fermat's last theorem is undecidable. It proposes probabilistic proof for
undecidable propositions. Moreover, the paper has an introduction to the
solution of the gravitational n-body problem presented at the World
Congress of Nonlinear Analysts, that same year and published in Nonlinear
Analysis, A-Series: Theory, Methods and Applications the following year.
(3).Exact Solutions of Fermat's Equation (Definitive Resolution of Fermat’s Last Theorem (FLT). Nonlinear Studies, 5(2), 1998, pp. 227 - 254.
Abstract. The inability to resolve this problem for 360 years is attributed to
the inadequacy of the underlying fields of FLT, namely, foundations, number
theory, the real number system and analysis. Their critique is undertaken
with special focus on Wiles' 127-page proof of this conjecture that bears all
the weakness of classical mathematics. The first major findings are: (1) FLT
is undecidable in arithmetic, the reals, and Rn, n > 1, (2) its underlying fields
are ill-defined and, therefore, FLT itself is ill-defined, and (3) the
characterization of undecidable propositions. It follows that FLT is not just
undecidable, it does not make sense in these spaces. Rectification includes
reconstruction of the real number system without the trichotomy and
completeness axioms. The new space, called the new real number system,
yields countable counterexamples to FLT proving that it is false. It resolves
all the problems, paradoxes, contradictions and unanswered questions of the
underlying fields except the Bieberbach conjecture and the Riemann
hypothesis.
(4) The Solution of the Gravitational n-Body Problem. Presented at the 2nd World Congress of Nonlinear Analysts, Athens, 1996 and published in the special issue of Nonlinear Analysis, A-Series: Theory, Methods and Applications, 30(8), Dec., 1997, pp. 5021 – 5032.
Abstract. The existence of long-standing unsolved problem reveals the
inadequacy of the underlying fields, in this case, mathematics and physics. A
thorough critique of both is undertaken. The main weakness of mathematics
lies in its foundations stemming from lack of insights coming from recent
discoveries such as the sources of ambiguity and lack of clarity regarding its
subject matter. Its critique led to the reconstruction of the contradiction-free
new real number system with new elements that models basic physical
concepts such as the superstring, the basic constituent of matter, the concepts
of time and distance and our universe as a super…super galaxy. The main
critique of physics is the inadequacy of quantitative or computational
modeling (previously called mathematical modeling) that simply describes
the appearances of nature. Consequently it has left long-standing problems
unsolved and fundamental questions unresolved such as what the basic
constituent of matter and the structure of the electron are. The remedy is the
introduction of qualitative modeling (formerly called dynamic modeling) that
explains nature in terms of its laws. This was the crucial factor in the solution
of the n-body and turbulence problems and resolution of fundamental
questions. Their solution and resolution required the discovery of the initial
11 laws of nature that anchored the early formulation of GUT called the flux
theory of gravitation.
(5) Superstring loop dynamics and applications to astronomy and biology. Nonlinear Analysis, Series A: Theory, Methods and Applications, 35(8), (1999); pp. 959 - 985.
Abstract. The paper refines the fundamental physical principles of (4),
includes four biological principles and introduces (a) dark number as the
qualitative model of the superstring, (b) the mathematics of its conversion to
visible matter, (c) matter-anti-matter dynamics, (d) applications to astronomy
and biology and (e) the new nonstandard analysis. It provides, for the first
time, explanation of two recent spectaculars from space made possible
nascent stars and galaxies and (ii) the "cannibalizing" activity of giant
galaxies, including our Milky Way, that prey on their smaller satellite
galaxies. Also, for the first time, the paper links brain waves to dark matter,
provides insights on the functions of the brain, including learning, memory
and intelligence, and proposes therapy for control of brain malfunctions like
autism.
(6) Set-valued differential equations and applications to quantum gravity, Proc. 1st International Conference on Tools for Mathematical Modeling; published in: Mathematical Research, Vol. 6, 2000, St.Petersburg, pp. 58 – 69.
Abstract. The paper starts with the practical problem of solving differential
equation of the form
dy/dx = f(x), where f(x) has the forms,
f(x) – sinn1/x, f(x) = cosn1/x, f(x) = (sinn1/x)cosm1/x,
and n and m are positive integers and the functions have set-valued limits at
the origin. The notions of probability distribution over the set-values and the
integral with respect to it are introduced to devise the generalized integral for
set-valued functions. Then the integral is applied to calculations on prima
and photons whose axial projections are set-valued.
(7) Recent verifications and applications, Proc. 1st International Conference on Tools for Mathematical Modeling, State Technical University of St. Petersburg, St. Petersburg, July 1999, pp. 74 – 89.
Abstract. The paper reviews present verification of the flux theory of
gravitation in quantum physics and astronomy and applies qualitative
modeling (formerly called dynamic modeling) to derive the structure of the
superstring and prima.
[8] Dynamic Modeling and Applications, Proc. 3rd International Conference on Tools for Mathematical Modeling, State Technical University of St. Petersburg, Russia.
Abstract. The paper summarizes recent verification and applications of the
then flux theory of gravitation to the study of the Cosmos, the solar system
and other applications but adds a new element to it: the role of the brain in
the control of cancer.
(9) Quantum Gravity. Proc. Third International Conference on Dynamic Systems and Applications, 26 ‒ 29 May 1999, released 2001, pp. 201 – 208.
Abstract. Quantum gravity is the dynamics of vortex flux of superstrings
induced by primal flux spin. It is distinguished from macro gravity as
dynamics of fluxes of superstrings. Quantum gravity encompasses quantum
physics and extends its domain to dark matter. It explains the genesis of the
atom where the toroidal fluxes of the protons in the nucleus induce coherent
flux around it; the latter draws electrons into orbit, by flux-pressure
complementarity. Quantum gravity explains all forces and interactions of
nature at the biological, molecular, atomic and primal levels including
electromagnetism, matter-anti-matter interaction, surface tension, osmosis
and capillary action in the cells of living organisms as well as primal
coupling and formation of the atom. The main laws of nature governing
quantum gravity are energy conservation, flux compatibility and flux-lowpressure
complementarity.
(10) Turbulence: Theory, Verification and Applications. Proc. 3rd World Congress of Nonlinear Analyst, Catania, 2000, published in the special issue of Nonlinear Analysis, Series A: Theory, Methods and Applications, 47(2001), pp. 5955 – 5966.
Abstract. The paper poses the turbulence problem: given the standard
dynamics find a model that has predictive capability with respect to its
internal and external dynamics and future state. The desired model is the
theory of turbulence, as subtheory of FTG, anchored on 12 of its
fundamental principles. The theory is applied to the study of earthquake,
volcanic activity, tornado, typhoon and lightning. The major results are as
follows:
(1) Solves the turbulence problem and explains the dynamics of earthly
turbulence.
(2) Establishes correlation between solar eclipse, earthquakes and volcanic
activity.
(3) Provides the basis for generating the technology to terminate tornado,
control typhoon partially and monitor seismic and volcanic activity that can
be the basis for prediction.
(4) Establishes the dynamic relationship between under-ocean volcanic
activity, El Niño, typhoon and drought.
(11) Chaos, Turbulence and Fractal. Indian J. Pure and Applied Mathematics, 32(10), pp. 1539 – 1551. (In the original paper this article is incorrectly titled, The flux theory of gravitation IV: The theory of intelligence and evolution).
Abstract. The turbulence problem in (9) is generalized to the modeling
problem: find a model for a physical system that has predictive capability on
its internal, external and future states. The paper starts with a criticism of
computational modeling namely:
(1) Computational model is static and unaffected by and not sensitive to
emerging boundary conditions including interaction with other dynamic
systems;
(2) It simply describes superficial dynamics but lacks predictive capability;
(3) Computation on the model simply reveals behavior of the mathematical
space the model belongs to and has nothing to do with the physical dynamic
system it models; in general computation, provides insights on differential
equations and the real numbers;
(4) Local behavior, especially, at micro scale has no causal relationship with
global behavior; for instance, the second law of thermodynamics that
predicts increasing entropy for closed physical system is valid only locally;
our universe has moved from the chaos of the Big Bang to the high level of
order we now enjoy including biological order; therefore, the first law of
thermodynamics is reversed globally.
(5) A differential equation which is indispensable in quantitative modeling
and its solution have only local validity, a basic principle in the theory of
differential equations. Conventional modeling is inadequate for dealing with
ambiguous sets including chaos, turbulence and fractal; it is shown also that
the real line is chaos. This paper identifies ambiguous sets and their common
thread of uncertainty and identifies appropriate approaches for dealing with
them. Among the ambiguous sets are large and infinite sets (being large and
small depending on context), small and large numbers, micro component of
turbulence, chaos and limit set of fractal. Deterministic mathematics does not
apply to ambiguous sets. This paper proves, for the first time, that the real
line is chaos. The alternative to computational modeling is qualitative
modeling, i.e., physical theory anchored on the laws of nature at both
fundamental states – dark and visible. Physical theory is not developed by
computation alone but is based on synthesis of the collective human
experience and accumulated scientific knowledge. The main tool for
qualitative modeling is qualitative or non-quantitative mathematics defined
broadly as the complement of computational mathematics. The paper also
summarizes the new mathematics required by FTG that, together with some
computational mathematics, e.g., Pontrjagin maximum principle, constitutes
its mathematical component.
(12) Theory of intelligence and evolution. Indian Journal of Pure and Applied Mathematics, 33(1), 2003, 111 – 129.
Abstract. Ten laws of thought are discovered to explain such capability of
the mind as learning and creativity. It explains how values are formed
including mathematical reasoning.
(13) The mathematics of the new physics. Applied Mathematics and Computation, 130(1), 145 – 169.
Abstract. With the terminating decimals as base space subject to the axioms
of the so-called complete ordered field, R*, +, ×, without the axiom of choice
or its variants, the standard topology is introduced. The space is extended
and completed to what is called the new real line with the standard topology.
The reconstructed new real line, R*, +, ×, has two new elements called dark
and unbounded numbers. The domain of the additive and multiplicative
operations is also extended to the new real line, R*, +, ×. The new real line is
further extended to the new nonstandard analysis. The paper refines and
extends the counterexamples to FLT to a combination of countable integers
and new integers (now called decimal integers). The new arithmetic is also
introduced as well as basic arithmetic of twin naturals, new integers and new
nonstandard analysis. The integers and new integers are shown to be
isomorphic; in this isomorphism 0 corresponds to the equivalence class of
dark numbers represented by d*. This isomorphism establishes that both the
integers and the new integers are Peano naturals. It is from this class of
numbers that the counterexamples to FLT are constructed.
(14) From macro to quantum gravity. Problems of Nonlinear Analysis in Engineering Systems, 7(1) 2002; pp. 56 – 78.
Abstract. The paper summarizes the work that starts with the solution of the
gravitational n-body problem and proceeds to develop gravitation in the
large, that is, gravitation at the astronomical scale. It is extended to gravity at
the atomic and biological scales called quantum gravity to form the flux
theory of gravitation (now GUT); it explains surface tension in liquids as
gravity at the molecular scale. The laws of nature are refined and some of the
mathematics of the superstring and black hole excerpted from [14,15} are as
follows:
Theorem 1. A curve of any length can be deformed continuously into an
oscillation in an infinitesimal neighborhood of a point with length preserved
or even enhanced.
Theorem 2. Given oscillatory curve K of any length, real number e > 0 and
line segment AB, there exists continuous deformation of K into a fine
oscillatory curve inside some neighborhood of a line segment which
preserves its length k.
Theorem 2 generalizes Theorem 1 since the segment AB can be confined to
an arbitrary neighborhood.
Theorem 3. Given any oscillatory curve K, there exists continuous
deformation of K, with length preserved, into an arbitrarily small
neighborhood.
Theorem 4. Let K be oscillatory curve of any length k and let b > 0, e = b/2
< K/2. One can shrink oscillatory curve K into arbitrarily small
neighborhood its length and amplitude satisfying │K│/2n+2 < │K│/2n+1 ≤
│K│/2n.
This theorem captures the behavior of superstrings and is the mathematical
basis of black hole formation. Since the energy of an oscillatory motion (e.g.,
superstring flux) is proportional to frequency and infinitesimal oscillation has
great frequency this deformation is energy enhancing and there is no upper
bound for the amount of latent energy in a superstring.
Finally, the paper has graphics of the well known prima, simple and
composite, including the quark, proton, and neutron, nucleus, basic cosmic or
electromagnetic waves and cosmic waves of Types I, II and III. It has also
graphics of generalized fractal.
The paper summarizes all previous papers by the author on gravitation. It
notes, for the first time, that the theory unites the three principal dynamics of
our universe, namely, macro and quantum gravity and cosmic waves where
the last dynamics spans the first two, and thermodynamics. It explains all
interactions of matter at the primal, atomic and biological scales including
electromagnetism, matter-anti-matter interaction, surface tension, osmosis
and capillarity action in the cells of living organisms. The paper also explains
all forms of clustering including the genesis of the atom and molecules and
stellar and galactic formation. It introduces three kinds of cosmic shock
waves: (1) Type I that includes brain waves, i.e., basic cosmic waves
encoded with information from neural cluster, (2) Type II cosmic waves,
e.g., shock waves from grinding of tectonic plates, stellar storms, stellar and
galactic core turbulence and hot volcanic lava flow (used in predicting
eruption) and (3) Type III cosmic waves, e.g., shock waves from nuclear and
thermonuclear explosions and cosmic explosions such as collisions of stars
called supernova and the Big Bang. Types II and III cosmic waves have the
same internal fractal structure but differ in orientation with respect to their
respective radius of propagation. The latter’s axis is normal to the radius of
propagation. The paper also formulates the nested fractal model of our
universe from the super…super galaxy through the superstring.
(15) Vortex interaction. Problems of Nonlinear Analysis in Engineering Systems, 7(2) 2002; pp. 30 –44.
Abstract. The paper develops the fractal-reverse-fractal algorithm that
allows one to locate, from any cosmological body, any other cosmological
body belonging to any cosmological vortex of our universe and, conversely,
from a vortex at any scale to the super…super galaxy, our universe.
(16) The new mathematics and physics. Applied Mathematics and Computation, 138(1), 2002, 127 – 149.
Abstract. The paper summarizes the new mathematics and FTG and some
astonishing results of mathematics. It has detailed critique of J. M. Henle’s
non-nonstandard analysis (Mathematics Intelligencer, 1999) and includes the
resolution of the unsolved problems, paradoxes, contradictions, puzzles,
contradictions and unanswered questions of mathematics, physics, astronomy
and cosmology except the Bieberbach conjecture and Riemann hypothesis.
Among the more notable problems, paradoxes and counterexamples resolved
and summarized here are: FLT, Goldbach’s conjecture, Brouwer’s
counterexample to the trichotomy axiom, Banach-Tarski paradox and the
natural or linear ordering of the new real line.
(17) Macro and quantum gravity, cosmic waves and applications. Applied Mathematics and Computation, 139(1), 2003, 23 – 36.
Abstract. The paper summarizes all previous results on the subject in the
Series on the subject and extends them as follows:
(a) Explanation of the accelerated rapid radial expansion of our universe
from FTG’s viewpoint.
(b) Verification of Hubble’s law in terms of the accelerated radial expansion
of our universe including an explanation of this phenomenon.
(c) Counterexamples to Einstein’s and Newton’s law of gravitation, namely,
cosmic debris such as asteroids and the thin rings of the larger planets of the
solar system.
(d) Lays down the cosmological history and destiny of our universe.
(e) Explains the primordial black hole that exploded as Big Bang as the
destiny of the core of previous universe and points to evidences of the
existence of universes other than ours.
(18) Dynamic (now qualitative) Modeling and Applications. Proceedings, 4th International Conference on Tools for Mathematical Modeling, St. Petersburg, 2003, 167 – 182.
Abstract. Axiomatizes turbulence using dynamic modeling (now qualitative
modeling) that explains gravity as part of its dynamics. It includes a
comprehensive explanation of why the Columbia Space Shuttle crashed on
February 1, 2003.
(19) Foundations of Analysis and the New Arithmetic. Nonlinear Analysis and Phenomena, 3(2), 2003, 13 pages.
Abstract. The paper reconstructs the real number system as decimals into the
new real number system without the trichotomy and completeness axioms
using the basic integers as building blocks (taking this as one of the axioms)
and well-defined by two more axioms – the addition and multiplication
tables of basic arithmetic. Taking the constructivist requirement that a real
number is well-defined only by its digits, that is, when they are known or
computable, we are able to build the new real number system without
contradictions and paradoxes. Among the findings are: the standard real
numbers (the decimals) are finite but unbounded (precise definition of
countably infinite), therefore, discrete, free from contradictions, have natural
ordering and enriched by the unique dark and unbounded numbers d* and u*,
respectively. This new construction suits the needs of computing, especially,
computer simulation, and physics since nature is discrete in view of the
recent discovery of the basic constituent of matter, the superstring.
(20) Dynamic Modeling (now qualitative) of Chaos and Turbulence. Plenary lecture at the 4th World Congress of Nonlinear Analysts, Orlando, 2004, Nonlinear Analysis, 63(5-7), 2005, e519-e532.
Abstract. Applies dynamic modeling to chaos and turbulence as part of the
standard dynamics and builds up the flux theory of gravitation as a general
theory of turbulence. It uses Hubble’s law to compute the present rate of
radial expansion of our universe which is 840 km/sec and its acceleration of
10−10.km/secsec. This is the rate at which matter in our universe, including
the galaxies is radially dispersing outward. The paper also explains the black
hole as massive cluster of non-agitated infinitesimal superstrings collected by
the eye of a macro vortex such as star or galaxy. Left alone, a superstring,
which is nested fractal fluxes of superstings, shrinks towards infinitesimal
superstring. This dynamics occurs in the calm, low-pressure region of the eye
of a macro vortex. It explains that a black hole does not suck matter; it is the
eye that nurtures and builds it up that does. Gravitational attraction itself is
due to the suction by vortex eye. The opposite dynamics is: when a semiagitated
superstring is hit by cosmic shock wave of suitable energy, it
converts to visible matter called primum, e.g., quark, electron and positron.
Furthermore, the paper reveals prototypes of technology that converts dark
matter to useful kinetic energy, electricity and magnetic repulsion presently
used to power magnetic train. (The values obtained here are based on the
corrected age of our universe – the original estimate of 8 billion years instead
of the current estimate of the age of our universe of 14.7 billion years.
(21) The New Frontiers of Mathematics and Science, Part I. Theoretical Construction and Resolution of Issues, Problems and Unanswered Questions, Nonlinear Analysis and Phenomena, Vol I, January 2004,1 – 26.
Abstract. The paper has the most detailed elaboration to-date of dynamic
modeling that led to the development of quantum and macro gravity. It welldefines
and explains ill-defined physical concepts and phenomena such as
quark, atom, black hole, dark matter and supernova.
(22) The pillars of the new physics and some updates. Nonlinear Studies, 14(3), 2007, pp 241 – 260.
Abstract. This paper summarizes the pillars of FTG, updates and uses FTG
to identify and rectify the errors of physics and highlights new applications
and explains the disastrous finite flight of the Columbia Space Shuttle. It
explains many puzzles of physics such as metal fatigue and corrects present
misinterpretation of certain phenomena such as thermonuclear explosion.
(23) The physics of the mind, accepted, The Science of Healing Outcomes.
Abstract. This paper explores the physics behind thought and sensation and
its implications for mathematics and physics and science education. It
explains telekinesis and other amazing capability of the mind such as that
displayed by what psychologists call moronic genius who computes huge
numbers without knowing how that happens. Most of all, it describes how
information is encoded, how they are recalled to the creative-integrative
region for thought and creativity.
(24) The New Frontiers of Mathematics and Science, Part II. The new real number system: Introduction to the New Nonstandard Analysis. Nonlinear Analysis and Phenomena, Vol. II, January, 2005, pp. 15 – 30.
Abstract. This is the first formal construction of the new real number system
R*, +, ´, using only three simple axioms: (1) R* contains the additive and
multiplicative identities, 0, 1; and (2) the addition and (3) multiplication
tables of basic arithmetic, and its extension to the new nonstandard analysis.
Limit in Bolzano-Weierstras sense (which is ill-defined) is replaced by
intuitive limit, that is, representation of a decimal by its standard Cauchy
sequence and approximating any decimal to any level of accuracy by the kth
term of its Cauchy sequence. The new real number system is finite but
unbounded (countably infinite) and, therefore, discrete, has no contradiction,
has natural ordering and is enriched by the unique dark number d* and
unbounded number u* and the new integers (now called the decimal
integers). The integers are embedded in R* which rectifies the fundamental
flaw of number theory, that of having no valid axiomatization of the integers.
In the new nonstandard analysis, every function is discrete. This suits the
needs of computing, especially, computer simulation.
(25) Dynamic Modeling (now qualitative) and the new mathematics and physics. Neural, Parallel and Scientific Computations, 15(4), 527 – 538.
Abstract. Surveys the classical and new mathematics involved in the new
physics, i.e., GUT, and highlights the role of the new mathematics.
(26) The origin and evolution of biological species. accepted, The Science of Healing Outcomes (a medical journal).
Abstract. The paper identifies brain waves as the medium for the replication
of the genetic content of biological species. It illustrates intelligence and
organization and division of labor in lower species and their further
advancement and defense against predators and ruminants that pasture on
them in the case of plant species, e.g., plant species that produce toxins. It
points to sensation as the basis of intelligence that allows a biological species
to respond to the environment, survive and advance itself. It illustrates, with
many examples, how species protect itself from other species that feed on it.
It also points out that instinct is genetically determined and explains how it is
actualized in plants and animals.
(27) Extending the reach of computation. Applied Mathematics Letters, 21(10), 2008, 1074 - 1081.
Abstract. The paper applies the new real number system to discrete
computation and quantum algebra.
(28) The theory of everything. Journal of Nonlinear Analysis and Phenomena, Volume II, No. 2, July, 2005, 44 pages (the author’s submission for his nomination for the Nobel Prize for Physics, 2005).
Abstract. This is an expository paper that summarizes and consolidates the
new physics developed in the flux theory of gravitation. The theory unifies
all the forces and interactions of nature from dark matter through quantum
and macro gravity and cosmology. (This was this host’s submission for his
nomination for the Nobel Prize for Physics, 2005)
(29) Dynamic (now qualitative) and mathematical models of physics. Proceedings of the 6th International Conference of Dynamics Systems, 2008; pp. 164 – 169.
Abstract. It provides dynamic and mathematical models of basic physical
concepts, particularly, the photon, quark, neutrino, electron, proton, neutron
and the nucleus.
(30) Basic physical concepts of the Hybrid Grand Unified Theory. Proc. International Conference on Recent Developments in the Mathematical Sciences and Applications, Dec. 25 – 28, 2009, GVP College of Engineering, JNT University, Vishakhapatnam, AP, India, 8 pages.
Abstract. Introduces the other inhabitants of our universe starting with the
superstrings and moving on to the prima, atoms, cosmological vortices and
black holes.
(31) By-passing Chaos With a Theory of Turbulence and Development. An article in the book, Finance Stochastics, World Scientific, London, 2001, edited by E. Perez, D. Bonzo (Eds.).
Abstract. This is the first axiomatic treatment of a new area of social
science, namely, development science. It uses the same technique in the
axiomatization of physics undertaken in the Series. Fundamental social
principles are identified to anchor development science. Based on this theory,
strategic positioning employed for the purpose of establishing scientific,
trade, economic and technological equity between the Third World and the
developed world, particularly, the developed countries. This is the strategy
for generating and accumulating tremendous accumulation of value to reach
the threshold for industrial development.
(32) Probability Distribution In Mathematics, The Philippine Statistician. 40. 1-2 & 3-4. 1991, pp. 47 – 56.
Abstract. Introduces probability distribution as a tool for integrating setvalued
functions.
(33) Qualitative model of the atom, its components and origin in the early universe, Nonlinear Analysis, C-Series: Real World Problems. 11(2009), pp. 29 – 38.
Abstract. This paper is the first qualitative model of the atom and its
components as well as its origin in our early universe. The atom’s
components – proton, neutron (with its neutrino) and electron – are built on
the prima, units of visible matter. Their qualitative models are obtained using
some laws of nature. They yield new information such as the mass of the
neutrino and how heavy isotopes of an atom form as well as the arrangement
of the nucleons. It clarifies some presently unresolved issues such as what
happens in thermonuclear explosion and whether it can be controlled to
generate energy. It also explains the wave-particle duality of the primum and
photon, metal fatigue, matter-anti-matter interaction and brittle and malleable
materials and reviews the early phase of the development of our universe up
to the formation of the first atom.
(34) Qualitative modeling for complex systems, Proc. 23rd International Conference on Operations Research, September 2009, Bonn, Germany, 10 pages (appears also in Problems of Nonlinear Analysis in Engineering Systems, in press).
Abstract. The paper introduces qualitative modeling for analyzing complex
systems and solving complex problems and explaining natural phenomena in
terms of natural laws. Its power is demonstrated by its role in the discovery
of the basic constituent of matter, the superstring, the key to the solution of
the gravitational n-body and turbulence problems. Qualitative modeling is
applied to the equally difficult problem of development using a similar
approach: discovering the relevant laws of society and production. The latter
includes laws governing creation, accumulation and distribution of value and
accumulation and utilization of surplus value. Then a theory of development
is devised for formulating a strategy for development of underdeveloped
countries. It notes that while the problem of underdeveloped countries is
underproduction, i.e., scarcity of social surplus, the problem of developed
countries is just the opposite: overproduction of commodities that cannot be
marketed leading to periodic disruption in the global economy called
recession or depression in its worst form. These opposites provide basis for
symbiotic relationship between the underdeveloped and developed countries
and devising a strategy beneficial to both based on advanced scientific
knowledge provided by the Grand Unified Theory to generate appropriate
technology as the principal component of development.
(35) The mathematics of the grand unified theory. Keynote address at the 5th World Congress of Nonlinear Analysis, July 2 – 9, Orlando, Florida, Nonlinear Analysis, A-Series: Theory, Methods and Applications, 71 (2009) e420 – e431.
Abstract. This paper surveys the mathematics of the Grand Unified Theory,
classical and new, and focuses on the construction of the new real number
system R*.
(36) The new real number system and discrete computation and calculus. Neural, Parallel and Scientific Computation, 17 (2009), 59 – 84.
Abstract: The paper points out the inconsistency and ambiguity of the field
axioms of the real number system and notes that the only clearly defined and
consistent mathematical model of the real numbers is the set of terminating
decimals. Inconsistency collapses a mathematical system since every
statement in it is contradicted by another. The inconsistence in the real
number system comes from the trichotomy and competeness axioms to
which counterexamples have been found To remove the inconsistency and
ambiguity the real numbers are built on the additive and multiplicative
identities 0, 1 and addition and multiplication tables of elementary arithmetic
as its axioms that define the operations addition and multiplication,
respectively. Then using 0 and 1 the terminating decimals are defined on
which the nonterminating decimals are defined for the first time (prior to this
the nonterminating decimals were simply arrays of digits most of which
unknown). The g-norm is introduced where the g-norm of a decimal is itself.
Then the g-closure of the terminating is the new real number system R* that
includes the nonterminating decimal and the set-valued nonstandard number
d* called dark number which is a continuum. Then the decimals are joined
together by the continuum d* so that R* is a continuum It is non-
Archimedean and non-Hausdorf but its subset of decimals countably infinite,
hence, discrete, Archimedean and Hausdorff. Highlighted in this paper are
the counterexamples to FLT that prove it false and the proof of Goldbach’s
conjecture.
(37) The grand unified theory. Nonlinear Analysis, Series A: Theory, Methods and Applications 69(3), 2008, 823 – 831. The paper is a contribution to the felicitation volume, special issue of Nonlinear Analysis on the occasion of 85th birth anniversary of Professor V. Lakshmikantham, founder of the broad and rapidlyexpanding field of nonlinear analysis and Editor-in-Chief of many renowned scientific journals.
Abstract. The paper is the first formal formulation and presents an overview
of the Grand Unified Theory, introduces the ten most important natural laws
and surveys the mathematics related to GUT’s development and applications
with more detail on the author’s recent contribution, the new real number
system.
(38) The generalized integral as dual of Schwarz distribution, in press, Nonlinear Studies.
Abstract. The paper develops the generalized integral and derivative of setvalued
function called wild oscillation using rapid oscillation for
approximation and deriving the probability distribution of wild oscillation as
set-valued function for purposes of generalized integration. It applies the
generalized integral to calculation on the photon
.
(39) Global geology and oceanography. Invited paper, International Journal of Earth Sciences and Engineering, in press
Abstract. The paper develops the theory based on GUT and applies it to lay
down the cosmological history of Earth. It explains the reversal of the
Earth’s magnetic flux during its 25,000-year cycle and the regular reversal of
Indian Ocean current with the summer and Winter Solstices.
(40) Revisiting the hybrid real number system, Nonlinear Analysis: Hybrid Systems, 3(2) May 2009, 101-107 (co-authored with Bhaskar, T. G., Kovak, D., Lakshmikantham V.).
Abstract. The new real number system is combined with Ancient Indian
thought to develop the hybrid real numbers.
(41) The unified theory of evolution, invited paper, International Journal of Biological Sciences and Engineering, in press
Abstract. Eleven laws of nature are discovered to update the theory of
evolution. Among the latest findings are:
[42] Genetic alteration, modification and sterilization and applications to the treatment of genetic diseases, accepted, The Journal of the Science of Heaibg Outcomes; 11 paages.
Abstract. The paper formulates the theory behind genetic alteration, modification
and sterilization based on the theory of evolution updated by the grand unified theory
(GUT). The key element in the updated theory is the discovery that the medium for
both the brain and the gene for doing their functions are brain waves, i.e., basic
cosmic waves encoded with the vibration characteristics of a living cell such as the
neuron or the cell of any tissue of living organism. The principal component of brain
wave is the vibration characteristic of the gene. It is established that the gene projects
brain waves that agitate and convert the superstrings in the cellular membrane to
molecules that form the tissues of living things. The gene is turned on to do this task
at the right place on cue from the environment there in accordance with the
biological law, genetic activation.
Then appropriate technology is proposed for treatment of genetic diseases such
as cancer, systemic lupos erythematosus, diabetes, muscular dystrophy and mental
disorder, e.g., depression, without injury to normal cells. The methodology is called
genetic modification; it uses a neutralizer gene to form a composite with the
defective gene that removes its symptoms. The neutralizer gene resonates with the
defective gene so that the brain waves it projects superperpose on the brain waves
projected by the defective gene to produce composite brain waves that do not show
the symptoms of the defective gene. In effect, a composite gene is produced without
the harmful symptoms. For cancer, however, a more appropriate and effective
treatment is genetic sterilization to prevent it from spreading to normal cells. Then
the sterilized cancer cells become harmless; they die in the normal turnover of cells.
Genetic alteration involves introduction of a gene that produces desirable
physical qualities such as the developed muscle of the weight lifter through the
beneficial application of the induced alteration law that says: the possible sources of
genetic alteration are: radiation (including the so called background radiation which
are cosmic waves), direct exposure to foreign gene, frequent, consistent and
sustained use of body part, chemical irritation and concentrated thought about and
pre-occupation with or craving for an object, living or not, during pregnancy.
Again, as in the previous papers, the methodology employed is qualitative
modeling.
(43) Extended Geometrical and Generalized Fractals, Chaos and Applications, a chapter in the ebook, Fractal Classification and Applications, in press, Nova Science Publishers.
Abstract. Starting with classical geometrical fractal in the plane we extend
present classical technique of affine transformation for generating fractal by
admitting other self-similar transformations, e.g., taking mirror image of
generator, sliding over a curve and rotation, where finite generators are
allowed. Such fractal is called extended geometrical. Geometrical fractal is a
sequence of composite affine transformations of a geometrical figure. Affine
transformation is a composite of contraction and translation. We further
extend geometrical fractal by broadening self-similarity to apply to general
properties beyond geometrical such as branching property and circular,
sinusoidal and vortical motion with applications to quantum and macro
gravity and thermodynamics of the grand unified theory (GUT). We focus on
generalized fractal and its applications to quantum and macro gravity and
thermodynamics of GUT.
Since general properties are not always amendable to computation, the
main tool of the present methodology of natural science – quantitative
modeling that relies solely on computation and measurement – the
appropriate methodology for GUT is qualitative modelling that relies on
qualitative mathematics. Our universe is a nested generalized physical fractal
with itself as the first term down through its fractal sequences that end up as
tail sequences of superstrings in dark matter.
In view of the updated scientific knowledge provided by GUT, we
reorient the priority in verifying validity of physical theory. We take as
primary criterion for validity its ability to explain natural phenomena and,
secondarily, invention of technology that works which requires prediction.
Moreover, we clarify some natural phenomena and make some predictions.
(44) Mathematical Models on the way from Superstring to Photon (Coauthored with V. V. Gudkov, Professor of Mathematics, Department of Computer Science and Mathematics, University of Latvia). Nonlinear Analysis, 3(2002), pp. 375 - 382.
Abstract. The paper applies FTG to the physical dynamics of prima
(elementary particles of quantum mechanics) and their clusters and
interactions. The prima considered are the electron, up and down quarks (the
second author uses right and left quarks, respectively, to stress the invariance
of toroidal flux spin and induced flux under radial deformation, translation
and rotation) and coupled prima like the neutrino, proton, neutron and the
nucleus of an atom. The basic mathematical model of a segment of
superstring is the helix as solution of the harmonic wave equation. Any
primal cluster and interaction can be modeled by suitable combination of
deformation, translation, rotation, reflection and attachment. The paper has
data on the tremendous latent energy of dark matter. For example, a cubic
meter of dark matter (vacuum of quantum mechanics) has latent energy
content of 1018 kilograms that is convertible to kinetic energy using
Einstein’s mass-energy equivalence equation. A fundamental physical
principle FTG is utilized here to suite the requirement of quantum gravity,
namely, the flux compatibility principle that governs primal clustering and
interaction.
(45) The Helix and Other Optimal Configurations of Matter and Applications (Co-authored with V. V. Gudkov). Nonlinear Analysis and Phenomena Vol. III, No. 2, 2006.
Abstract. The paper provides both qualitative and computational models of
the common prima like the proton and neutron.
(46) Sustainable Economic-Industrial Development for Underdeveloped Countries (co-authored with Chandra Prakash Kamana, first author, and V.S.R.S. Sarma Salagrama), Proceedings, International Conference on “Accelerating Economic Revival Through Innovation and Reform” Feb. 5, 6, 2010, organized by the Department of Commerce and Industry, Corporate Economics and Management Studies and Women’s Christian College, Chennai, India.
Abstract. Proposes Strategic Positioning as the only strategy for sustainable
development of the Third World in the present situation (see the article,
Primer on Strategic Positioning on this website)
(47) Building Green to Attain Sustainability (co-authored with Chandra Prakash Kamana, first author, andV.S.R.S. Sarma Salagrama), Proceedings, International conference on "Emerging Trends in Engineering (ICETE-2010)”, 20 – 21 February 2010, organized by Dr.J. J. Magdum College of Engineering (JJMCOE) in technical collaboration with Cafet-Innova Technical Society, in Dr. J. J. Magdum College of Engineering, Jaysingpur, Kolhapur District, Maharashtra, India.
Abstract. Points the way to find the lynchpin technologies for Strategic
Positioning that can partake of the enormous global resources into a Third
World Country for its sustainable development.
(48) Building Green – Practices and Challenges (co-authored with Chandra Prakash Kamana, first author and V.S.R.S. Sarma Salagrama). Proceedings of the International Conference on Environmental Sustainability with Green Building Technology (ICESGBT-10), 15 – 17 March 2010, organized by the Department of Civil Engineering, Meenakshi Sundararajan Engineering college, Chennai, India.
Abstract. Identifies the advantages of green building technology with
respect to energy consumption, and comfort and convenience.
(49) Geometrical and Generalized Fractals, Chaos and Turbulence and Applications, chapter contribution to the book, Fractal Classification and Applications, in press, Nova Science Publishers, 53 pages.
Abstract. Starting with classical geometrical fractal in the plane we extend
present classical technique of affine transformation for generating fractal by
admitting other self-similar transformations, e.g., taking mirror image of
generator, sliding over a curve and rotation, where finite generators are
allowed. Such fractal is called extended geometrical. Geometrical fractal is a
sequence of composite affine transformations of a geometrical figure. Affine
transformation is a composite of contraction and translation. We further
extend geometrical fractal by broadening self-similarity to apply to general
properties beyond geometrical such as branching property and circular,
sinusoidal and vortical motion with applications to quantum and macro
gravity and thermodynamics of the grand unified theory (GUT). We focus on
generalized fractal and its applications to quantum and macro gravity and
thermodynamics of GUT.
Since general properties are not always amendable to computation, the main
tool of the present methodology of natural science – quantitative modeling
that relies solely on computation and measurement – the appropriate
methodology for GUT is qualitative modeling that relies on qualitative
mathematics. Our universe is a nested generalized physical fractal with itself
as the first term down through its fractal sequences that end up as tail
sequences of superstrings in dark matter.
In view of the updated scientific knowledge provided by GUT, we reorient
the priority in verifying validity of physical theory. We take as primary
criterion for validity its ability to explain natural phenomena and,
secondarily, invention of technology that works which requires prediction.
Moreover, we clarify some natural phenomena and make some predictions.
(50) The Big Bang and What it Was, Chapter Contribution to the ebook, The Big Bang: Theory, Assumptions and Problems, in press, Nova Science Publishers. 56 pages
Abstract. The paper takes as its premise the occurrence of the Big Bang, a
colossal explosion that gave rise to the birth of our universe. Then through
sequences of mathematical and scientific reasoning called rational thought
using the methodology of qualitative modeling the grand unified theory
(GUT) is developed on laws of nature which establishes what it was that
exploded. This is a new approach. In earlier development both the
occurrence of the Big Bang and what caused it were taken as premises.
In its present development GUT builds its pillars – quantum and macro
gravity and thermodynamics. Through the discovery of appropriate laws of
nature, GUT well defines its fundamental physical concepts such as the
superstring, basic constituent of matter; matter and energy; dark matter; and
charge and gravity. It also well-defines and explains other physical concepts:
primum, photon, matter-anti-matter interaction, atom, cosmic waves, brittle
and malleable materials, metal fatigue, turbulence, galaxy, black hole and
supernova along with the conversion of dark to visible matter.
The cosmology of our universe is traced from its birth at Cosmic Burst 1.5
billion years from the start of the Big Bang through its evolution to the
present as a super…super galaxy 1010 billion light years across and a local
bubble in the timeless boundless Universe and predicts its destiny as black
holes back in dark matter. The existence of universes other than ours is
established from available evidences. Then it is deduced from this
cosmology what the Big Bang was and what caused it.
(51) Our Fractal Universe and Applications. Invited keynote address at the 6th International Conference on Dynamic Systems and Applications, May 25 – 28, Atlanta, USA, to appear in the proceedings. 8 pages.
Abstract. The generalized nested fractal structure of our universe is
described with itself as the common first term. A common feature of every
cosmological vortex is the family of spiral trajectories that simply covers it
along which visible matter falls through and spins around its eye. The
Integrated Pontrjagin Maximum Principle is applied to find the equation of
such a trajectory and solve practical problems.
II. Books and Monographs
(52) Introduction to Qualitative Control Theory. Kalikasan Press, Manila, 1991, 151 pages.
Abstract. This is the first development of qualitative or noncomputational
mathematics applied to control theory. It focuses on the properties of relaxed
trajectories and makes slight improvement of L. C. Young’s integrated
Pontrjagin maximum principle.
(53) On the undecidability of Fermat’s last theorem, monograph published by the Press Center, University of the Philippines Los Baños, 1993. 40 pages
Abstract. The first broad sweep of the partial resolution of this problem
which establishes its undecidability, reformulates it as a problem in R3
and
provides the probabilistic solution to the reformulated problem. The question
of truth of FLT is not considered here.
(54) Introduction to Qualitative Control Theory, Kalikasan Press, Manila, 1991.
Abstract. Adapts qualitative mathematics and modeling (introduced and the
main contribution of this author’s Ph.D. thesis, The Trajectories, Reachable
Set, Minimal Level and Chain of Trajectories in a Control Systme, at the
University of Wisconsin) to control theory. It has also a slight improvement
of L. C. Young’s Integrated Pontrjagin Maximum Principle.
(55) Diophantus: Introduction to Mathematical Philosophy (With Resolution of Fermat and Other Applications). Kalikasan Press, Manila, 1993, 156 pages.
Abstract. The resolution referred to here is probabilistic solution that says:
with probability 1, FLT is true when n > 2. The book makes a thorough
critique-rectification of mathematics including lack of awareness of the loss
of certainty in infinite and very large spaces in mathematical and scientific
pursuit. It introduces a totally new mathematical perspective. Several
counterexamples to the axiom of choice are given. The calculus of set-valued
functions is more fully developed and applied to oscillatory differential
equations. A general theory of fractal provides some of the basic
requirements towards the solution of the gravitational n-body problem. The
book has the first partial resolution of Fermat's last theorem as undecidable
in arithmetic, the reals and the Euclidean plane and the probabilistic solution
of the reformulated problem in R3. It points the way for dealing with
undecidable proposition (proposition having no deterministic proof): the use
of probabilistic mathematics. A critique of Wiles' initial offering of 1993
made it to the appendix while the book was in press. It is the first to point out
that Wiles' main error is lack of insights from recent discoveries in
mathematics such as characaterization of undecidable propositions and the
loss of certainty in infinite or very large spaces.
(56) The Hybrid Grand Unified Theory, co-authored with V. Lakshmikantham and S. Leela and published by Atlantis (a division of Elsevier Science, Ltd.), 2009; 185 pages. (Currently on the World Scientific
best sellers list since May 2009; got on the #2 spot on the list in July in all categories; #1 on the best sellers list in mathematics as of October 3, 2009)
Abstract. The book updates the foundations of mathematics and applies the
new real number system to develop the hybrid real number system. The main
chapter, The Grand Unified Theory, formulates builds GUT on macro and
quantum gravity using the new methodology of qualitative modeling. Then
both qualitative mathematics and GUT are applied to develop the theory of
turbulence and physics of the mind. The book concludes with an overview of
the grand unified hybrid system that combines modern and ancient scientific
thought.
(57) Scientific Natural Philosophy, an ebook in press, Bentham Science Publishers, 2010, 305 pages.
Abstract. The aim of philosophy is to provide a total view of an aspect of
reality, for our present pursuit, nature, the domain of natural science.
Naturally, that view is relative to the level of advancement of the field of
science concerned. The most important component of philosophy is
methodology for it determines the nature of knowledge that can be achieved.
For example, the current methodology of physics – quantitative modeling –
describes the appearances of nature mathematically in terms of numbers,
equations, functions or statistical trends. Thus, the knowledge it provides is
only descriptive. In biology species are classified on the basis of their
appearances, e.g., anatomical structure. However, this methodology has
limitations and left long standing problems of physics unsolved and
fundamental questions unanswered such as the gravitational n-body problem
and what the basic constituent of matter and the structure of the electron are.
The introduction of qualitative or non-quantitative modeling that explains
nature in terms of its laws not only solves and answers the long standing
problems and fundamental questions but also deepens our knowledge beyond
the appearances. It tells us how nature works and allows us to explain the
internal dynamics and interactions of physical systems. It also allows us to
devise technology guided by theory instead of appearances and properties of
materials. At the core of both methodologies are mathematics, qualitative
mathematics for qualitative modeling and computation and measurement for
quantitative modeling. Therefore, mathematics is not only a language of
sciences but also its indispensable tool for analysis. Consequently,
mathematics plays a major role in philosophy as part of methodology and we
shall devote a major part of this book to it.
Scientific natural philosophy is an updated philosophy of natural science
different from and an improvement of all previous ones because it is based
on major scientific development, innovations and discoveries during the last
12 years among which are the following:
(1) First and foremost was the introduction of qualitative modeling (formerly
called dynamic modeling) in 1997 to solve the 200-year old gravitational nbody
problem posed by Simon Marquiz de Laplace at the turn of the 18th
Century. It explains nature and its dynamics, appearances, properties and
motion in terms of its laws (natural laws). It is the complement of
quantitative modeling (formerly called mathematical modeling). The main
tool of qualitative modeling is qualitative mathematics and that of
quantitative modeling its complement, the combination of computation and
measurement. Qualitative mathematics includes this daily activity of the
mathematician or scientist: making conclusions, visualizing, trial and error,
thinking backwards, thought experimenting, engaging in creative activity,
intuition and imagination, negating what is known to find an opening into the
unknown, altering premises to draw out new conclusions and any technique
that yields results. It liberates the mind from unnecessary constraints and is
the key to productive research. Abstract mathematical systems such as
foundations, topology and the search for the laws of nature are qualitative
mathematics. It is based on rational thought and analysis, quantitative
mathematics on intuition. Consequently, qualitative modeling is also based
on rational thought and analysis, quantitative modeling on intuitions.
(2) Since qualitative mathematics has liberalized the search for information
for purposes of knowing nature and explaining its behavior and appearances
it also increases the chance of error creeping into physical theory. Error
includes contradiction, ambiguity, inadequacy and self reference. Therefore,
to avoid error we tighten the filter of admissibility in the choice of concepts
and axioms in the development of physical theory. In particular, we identify
the sources of error to avoid them.
(3) To solve a long-standing problem or resolve unanswered question we
find out why it defies solution or resolution and the first to check are its
underlying fields. Therefore, we go through their critique-rectification to
clear them of errors. This was the crucial first step in both the resolution of
Fermat’s last theorem [and the solution of the gravitational n-body problem.
(4) Qualitative modeling led to two important developments: (a) the
discovery of the existence of two fundamental states of matter, dark and
visible or ordinary matter, where the latter is directly observable and the
former is not and known only by its effect on visible matter and (b) the
discovery of the basic constituent of matter, the superstring.
(5) Qualitative modeling has also led to important discoveries in biology
aside from the biological laws. One is the discovery that the brain and the
gene have the same medium for doing their functions, namely, brain waves,
i.e., basic cosmic waves encoded with the vibration characteristics of living
cells. The main function of the brain is to control all body processes and its
secondary function is providing the venue for thought processes. The gene’s
main function is to produce the tissues of plants and animals in the cellular
membranes through the agitation of dark matter by the brain waves it
projects and their conversion, first to prima, then to atoms and molecules and
finally to the atoms and molecules of the tissues.
(6) Physical theory is a qualitative model of reality, in particular, nature. It is
a mathematical system whose basic premises or axioms are laws of nature.
Being so, any theoretical error is ultimately mathematical. While
mathematics, erroneous or not, is totally harmless and essentially useless in
the mind or its representation, mathematical error may have catastrophic
impact in the real world through the application of erroneous or absence of
theory. Therefore, we have given considerable effort to avoid mathematical
error by identifying its sources and avoiding them or providing remedy. We
cite disastrous failures in applications due to theoretical error.
(a) The disastrous final flight of the Columbia Space Shuttle, February 1,
2003 as being due to inadequate theory. In fact, in trying to explain why the
disaster occurred three new laws of nature were discovered. In particular, the
recurrent peeling of the insulation panels from the Shuttle when the
Columbia Space Shuttle Program was resumed after two and a half years of
suspension was never explained because there was no theory to do so. The
program was scrapped for this reason [34].
(b) The failure to make a breakthrough in plasma research towards
controlling thermonuclear reaction. After over half a century of this research
no significant breakthrough has been made.
(c) Research in particle physics in search of the basic constituent of matter.
Physicists have steadily raised the energy of the collider but they have not
found even a candidate for basic constituent of matter since all they found
are unstable elementary particles with half-life of split second. The basic
constituent of matter must be indestructible otherwise our universe would
have collapsed a long time ago. The large hadron collider in Cerne,
Switzerland was supposed to have been turned on last summer but there has
been no report on it so far. Like thermonuclear research this has been going
on for over half a century. Actually, the superstring has been staring at the
physicists since 1811 when Ernest Rutherford discovered the electron, an
agitated superstring.
(d) Cancer research. Geneticists and oncologists have been trying to
understand this genetic disease for the purpose of developing the most
effective treatment with the least side effect; this has been going on for a
long time but no significant breakthrough has been registered so far, a case of
lack of appropriate theory.
In each of these cases the culprit is theoretical error that includes erroneous,
inadequate and absence of theory to guide the research.
Although 6(b), 6(c) and 6(d) are not as catastrophic as 6(a), the enormous
amount resources, human and material, allotted to such failed research could
have alleviated the desperate conditions in much of the Third World.
(7) The 11 laws of nature discovered in 1997 required to solve the
gravitational n-body problem served as the initial axioms of the flux theory
of gravitation which was later corrected and named the grand unified theory
(GUT).
These are innovations, discoveries and advancement that distinguish the
grand unified theory, which we now summarize and call the new physics,
from all previous physical theories. It is much broader and more general than
what Albert Einstein envisioned which was to describe gravity and
electromagnetism by equations of the same form although this was modified
by quantum physicists who joined in to include the strong and weak forces of
physics in the unification. The grand unified theory that we now have is
stronger and much broader for it explains the forces and interactions of
nature and its appearances and, therefore, unifies as well the entire fields of
natural science. It raises the quality of scientific knowledge from description
of appearances of nature to knowledge of how nature works that includes
explanation of its appearances. Research is in progress to broaden GUT
beyond its pillars – macro and quantum gravity and thermodynamics – and
into the grand unification of natural dynamics where natural dynamics
includes interactions between physical systems and the latter broadened to
include all motions of matter such as cosmic waves, the synchronized
vibration of dark matter. This will not qualitatively alter scientific natural
philosophy based on GUT for there is no change in perspective and
methodology, only extension of domain.
All these developments are synthesized and integrated into scientific natural
philosophy. It is distinguished from all previous philosophies of science
because it is scientific in contrast to being speculative where the former rests
on scientific knowledge. In particular cosmology is no longer speculative but
knowledge provided mainly by macro gravity. Moreover, it is complete as it
provides a full account of the evolution of our universe from its birth at
Cosmic Burst to its destiny as cluster of black holes back in dark matter.
Every application of GUT to solve a scientific problem requires the
discovery of appropriate laws of nature to provide the solution. Thus, the
application of GUT to explain the disastrous final flight of the Columbia
Space Shuttle added three more natural laws to the theory of turbulence [23]
to advance it to the enriched theory of turbulence. In trying to understand the
role of the gene in the evolution of biological species and how it produces
the tissues of a living thing 11 biological laws were discovered to develop
the theory of evolution based on GUT. Five learning principles were also
discovered in the applications of GUT to investigate the brain’s functions.
This is an aspect of innovation in scientific methodology. In traditional
methodology existing knowledge is applied to solve some problems. Here,
given a scientific problem a theory is devised to provide the solution.
Therefore, in this new methodology a scientific problem serves as catalyst
for the advancement of science. It is clear that physical theory is the
embodiment of our knowledge of the domain of a field of natural science and
that without a theory we have, at best, a collection of information about it.
We have some new knowledge that enriches scientific natural philosophy:
(1) The laws of nature are transitory and their manifestation is simultaneous
with the respective emergence of physical systems or natural phenomena that
reveal them. For example, the biological laws that we now enjoy were nonexistent
immediately after the cosmic burst when only simple prima (a
primum is unit of visible matter) existed. They will all vanish as our universe
reaches its destiny as cluster of black holes.
(2) Our universe is a local bubble in the boundless and timeless Universe of
dark matter and there is ample evidence of the existence of other local
universes like ours. There are two kinds of local universes: ordinary resulting
from the steady shrinking of the superstrings that gives rise to nested fractal
sequences of regions of depression that, in turn, evolve into nested fractal
sequences of cosmological vortices of superstrings like the galaxies and
stars, and special universes like ours whose birth was triggered by a big
bang. A big bang is explosion of a black hole, the destiny of a previous
universe. Our universe was due to the explosion of a black hole, the destiny
of the core of a previous universe that created a super…super depression in
dark matter that evolved into a super…super galaxy 1010 light years across.
(3) GUT has brought us to the threshold of a new technological Epoch, the
epoch of GUT technology that runs on dark matter directly or indirectly.
Examples of the former are the magnetic train and the electric power plant
both of which run on fluxes of superstrings. Like the steam engine which
was invented before the development of the science of thermodynamics they
were invented before the development of GUT based on knowledge of the
property of the material used, mainly magnet. Therefore, they are considered
conventional. An example of GUT technology is the electromagnetic engine
for mass transit system. Its invention which is still at the research and
development phase is directly guided by GUT (the invention can only be
announced; details cannot be discussed at this time). Another example which
is still at the research stage (not even at research and development) is the
appropriate technology for genetic alteration, modification and sterilization
for the treatment of genetic diseases.
We provide selective theoretical applications of GUT and its methodology of
qualitative modeling that spill over into several fields of natural science and
its boundary with psychology – physical psychology.
Finally, scientific natural philosophy is materialist and focuses on
explainable physical reality.
In the Pipelines: An ebook, Symposium on the Grand Unified Theory, for
Nova Science Publishers; probable completion: 2012.
******* ******* *******
PUTTING THE INSTITUTE OF MATHEMATICS IN ITS PLACE
In 2005 the Philippine Collegian published the article, STATEMENT FROM THE UP
MATHEMATICS DEPARTMMENT, attacking me personally for my work in mathematics and
physics the argument based on wrong information and ignorance of mathematics and physics.
Fortunately, the Philippine Collegian which adheres to journalistic ethics published my reply, TOTAL
IGNORANCE OF FUNDAMENTALS. This cannot be said of the UP Newsletter which published
the same statement but did not publish my reply revealing itself as a gossip sheet after all. My mole at
the Department told me that the Chairman tried to solicit signatures for the statement from its over
100 faculty members but got only 7 the reason it was published anonymously.
Then in March 2008 another online article, Personal Statement from UPD, was addressed to me,
again, attacking my work by repeating the same old futile arguments but this time focusing on my
resolution of Fermat’s last theorem.
Now, there is a post on a page in the WikiPilipinas website, again, addressed to me and my work that
repeats the same old arguments which I have already resoundingly demolished on many websites.
WikiPilipinas, by the way, has published online on the same webpage outright lies about Filipino
inventors and scientists who are long gone and cannot defend themselves. It labelled as hoax the
inventions of Agapito Flores, Eduardo San Juan and Fe de Mundo without any documentation
whatsoever. It made a blunder, however, by also publishing on the same webpage lies about me, the
Manny Pacquiao of Science and Mathematics with Teflon world academic stature. When I posted this
message in reply the administrator, J. Maguddayao, deleted the entire entries and blocked my
username.
These online articles by the Institute of Mathematics amount to a tiny squeak behind the thousands of
articles, posts and commentaries on my work on several dozen websites not to mention my over 50
scientific papers in many world renown peer reviewed international scientific journals, keynote
addresses at world congresses and international conferences, books and chapters of some books. My
work has been extensively debated across cyberspace since 1997 and not a single hole has been
punched on it. All arguments against my work have been thoroughly demolished including these
feeble attempts by the Institute. Samples of my latest punches can be viewed at these sites:
(1) False Proofs, http://falseproofs.blogspot.com/2006/06/e-e-escultura.html
(2) Free Library, http://www.thefreelibrary.com/E.+E.+Escultura/Contributed-a274787
(3) http://scientopia.org/blogs/goodmath/2011/02/10/e-e-escultura-and-the-field-axioms/#comment-
27520
(4) New Approach to Physics, under ISCID topic Brainstorms (5 pages):
(a http://www.iscid.org/boards/ubb-get_topic-f-6-t-000607.html
(b) http://www.iscid.org/boards/ubb-get_topic-f-6-t-000607-p-2.html
(c) http://www.iscid.org/boards/ubb-get_topic-f-6-t-000607-p-3.html
(d) http://www.iscid.org/boards/ubb-get_topic-f-6-t-000607-p-4.html
(e) http://www.iscid.org/boards/ubb-get_topic-f-6-t-000607-p-5.html
If these feeble attempts by the Institute are a tiny squeak, why take notice? One reason is to take note
of a new trick proudly discovered by the Institute: creating the link,
http://en.wikipilipinas.org/index.php?title=User:Eescultura, to my article in WikiPilipinas with this
message (quoted verbatim including grammatical errors):
To whom it may concern;
I Edgar Escultura formally renounce my claims to have disproven Fermat’s Last Theorem (FLT), my
claims that the real number system is flawed, and my claim that the complex number i is not well
defined. I also retract my claim that Dr. Wiles acknowledged my work was correct and my claim to
have been nominated for the Nobel Prize in physics, I have discovered that these were both cruel
tricks being played on me by people signing a guestbook on my website.
I would like to acknowledge the efforts of various bloggers and their readers for taking the time to
demonstrate the flaws in my arguments. Were it not for their genuine care and patience I would still
be defending indefensible claims. I also apologize to any people who spent considerable time trying to
understand my writing, I was wrong and am man enough to admit it.
I would also like to inform the mathematics community that the journal that published my work,
Nonlinear Studies, did a grave disservice to you all in allowing work so peppered with errors to ever
be printed. I apologize for myself and the irresponsible behaviour of Nonlinear Studies.
Finally to Dr. Wiles, I offer you my sincerest apologies. Your proof is and always was correct, there
were no “fatal flaws” in it as I so often asserted. I also apologize to you for trying to pass off obvious
forgeries as your writings. Most importantly I would like to apologize to you for ever attacking your
stature as a mathematician, my claims were not only false but also inconsiderate, I acted foolishly and
can only hope you can forgive me.
E. E Escultura Research Professor V. Lakshmikantham Institute for Advanced Studies and
Departments of Mathematics and Physics GVP College of Engineering, JNT University
=================
This “apology” is, of course, FAKE. I NEVER POSTED IT and I DID SOMETHING MUCH
GREATER THAN SIMPLY MAKE A CLAIM: I ACTUALLY DISPROVED FLT by
counterexamples published in my papers in several renowned peer reviewed scientific journals. It is
also discussed in my recent books, Scientific Natural Philosophy (Bentham Science Publishers) and
Hybrid Grand Unified Theory (Atlantis, a division of Elsevier Science, Ltd) .When I posted this reply
on WikiPilipnas website it was deleted but the fake apology was retained although edited and toned
down a bit. Still, it is even worse than libel. Moreover, my username has been blocked from that link
and I cannot post my replies. Only the administrator, J. Maguddayao, could have done these changes
in connivance, of course, with the Institute.
The abstracts and summary of my publications are posted on one of my websites, Grand Unified
Natural Dynamics, http://users.tpg.com.au/pidro/ (see also my other website, Grand Unified Theory,
http://edgareescultura.wordpress.com/) Most of my papers are being sold online (for instance, search:
escultura science direct elsevier) and several of my papers have made it to the top 25 most
downloaded papers published by Elsevier Science Ltd in its several scientific journals. The latest
confirmation of my nomination for the Nobel Prize for Physics in 2005, which was dismissed by the
message from the Institute in WikiPilipinas, is the announcement online of my new book, Hybrid
Grand Unified Theory, co-authored with V. Lakshmikantham and S. Leela, published by Atlantis in
March 2009 and distributed by World Scientific which specifically mentions the nomination. This
book was a best seller in 2009 among books of all categories in natural and social sciences distributed
by World Scientific. It made it to the #2 spot on the best sellers list in July, 2009. For the information
of the Institute some of my major achievements recorded and etched in internet archives are as
follows:
1. Disproved Fermat’s last theorem by countably infinite counterexamples, Nonlinear Studies, 5(2),
1998, pp. 227 – 254 (published by the International Federation of Nonlinear Analysts).
2. Solved the gravitational n-body problem, Nonlinear Analysis, A-Series: Theory, Methods and
Applications, 30(8), 1997, pp. 5021 – 5032 (published by Elsevier Science, Ltd).
3. Solved the turbulence problem in, Turbulence: Theory, Verification andAapplications, Nonlinear
Analysis, A-Series: Theory, Methods and Applications 47(2001), pp. 1539 – 1551.
4. Discovered the superstring, basic constituent of matter, Nonlinear Analysis, A-Series: Theory,
Methods and Applications, 30(8), 1997 (this discovery is the foundation of the solution of the
gravitational n-body problem and the grand unified theory).
5. Developed the grand unified theory in a series of papers since 1997 and consolidated in the paper,
The Grand Unified Theory, Nonlinear Analysis, A-Series: Theory, Methods and Applications,:69(3),
2008, pp. 823 – 831 5032.
6. Developed the new real number system in a series of papers and consolidated in the paper, The new
real number system and discrete computation and calculus, Neural, Parallel and Scientific
Computations, 17(2009), 59 – 84 (Published by Dynamic Publishers).
7. Proved Goldbach’s conjecture, Applied Mathematics and Computation, 138(2003), pp. 145 - 169
(published by Elsevier Science, Ltd).
8. Developed the generalized integral for set-valued functions, Proceedings of the International
Conference on Tools for Mathematical Modelling, June 2000, St. Petersburg, Russia, pp. 221 - 224.
9. Developed the generalized integral as dual of Schwarz distribution, in press, Nonlinear Studies,
invited paper.
10. Developed the Complex Vector Plane which rectifies the present defects of the complex number
system in the appendix to: The generalized integral as dual of Schwarz distribution, in press,
Nonlinear Studies, invited paper; it is also summarized in the ebook, Scientific Natural Philosophy.
11. Gave a keynote address at the 5th World Congress of Nonlinear Analysts, Orlando, Florida, July 2
– 9, 2008 (Sponsored by the International Federation of Nonlinear Analysts); on the topic, The
mathematics of the grand unified theory, published in Nonlinear Analysis, A-Series: Theory: Method
and Applications, 2009, 71, pp. e420 – e431.
12. Gave another keynote address at the 7th International Conference on Dynamic Systems and
Applications, on the subject: Our Fractal Universe and Applications, May 25 – 28, 2011, Atlanta (the
abstract is published online).
13. Addressed a plenary session of the 5th World Congress of Nonlinear Analysts on the topic, The
new real number system as the g-closure of the terminating decimals, Orlando, Florida, July 2 – 9;
this paper was integrated in the original paper, The new real number system and discrete computation
and calculus (see item 6 above).
14. Gave a keynote address at the 4th International Conference on Dynamic Systems and Applications,
on the topic, Dynamic and mathematical models in physics, Atlanta, USA, April 30 – May 2, 2007
(the abstract is online).
15. Gave a keynote address at the 5,th International Conference on Neural, Parallel and Scientific
15. Introduced the new scientific methodology of qualitative modelling as the main contribution of
my Ph.D. Thesis, The trajectories, reachable set, minimal levels and chains of trajectories of a control
system, at the University of Wisconsin, 1970; it was applied to physics for the first time to solve the
gravitational n-body problem, 1997.
16. Made the first qualitative model of the atom in the paper, Qualitative model of the atom, its
components and origin in the early universe, Proc. 5th World Congress of Nonlinear Analysts, and
published by, Nonlinear Analysis, B-Series: Real World Applications, 2009, 11, pp. 29 – 38
(published by Elsevier Science, Ltd).
17. Developed the generalized fractal in the paper, Extended geometrical and generalized fractal,
chaos and turbulence, a chapter to an ebook, Fractal Classification and Applications, in press, Nova
Science Publishers.
18. Provided the first full explanation of the Big Bang in the paper, The Big Bang and What It Was, a
chapter in the ebook, The Big Bang: Theory, Assumptions and Problems, in press, Nova Science
Publishers.
The other reason for this article is to identify the sources of frustration that led to this futile and
desperate action by the Institute and provide insights on why the Institute stooped to ground level by
posting the fake apology quoted above. The brief history of the Institute below and its present status
sheds light on this strange behaviour.
(1) In 1986 I returned from the US after an absence of 15 years due to the political turmoil in the
Philippines during that period and re-joined the Department of Mathematics as Associate Professor.
(2) Eager to advance mathematics in the country I proposed in 1988 the conversion of the Department
from a purely teaching department to an Institute with stress on research.
(3) This proposal did not sit well with the leadership for obvious reason: no one else was doing
research at that time and the cloud of insecurity loomed large over it. The fall out: my dismissal from
the Department by denying tenure followed by sustained campaign of vilification that continues to
this day.
(4) What is the score? The Institute’s website reveals the following information:
(a) The Institute has 10 full professors, 7 associate professors, 9 assistant professors, one adjunct
professor, 56 instructors and many lecturers.
(b) NONE OF THE FULL, ASSOCIATE AND ASSISTANT PROFESSORS HAS ANY
PUBLICATION IN MATHEMATICS. The adjunct professor has publications in applied mathematics
which is commendable but not in mathematics.
(c) There are 20 papers by the adjunct professor and graduate students (with co-authors abroad) on the
applications of mathematics to other fields such as biology and computer science. They are also
commendable contributions to the fields of application of mathematics but not to mathematics. In
other words, after having enjoyed generous research grants as an institute, the Institute of
Mathematics has not produced even a single paper in mathematics during all those years. (It would be
more appropriate for this unit of the University to call itself a Department of Applied Mathematics;
ironically, it tries to train mathematicians and claims to be the leader in mathematical research)
In contrast, both the Marine Science Institute and the National Institute of Physics have hundreds of
publications each in per reviewed scientific international journals followed by the Institute of Biology
that has also substantial publications. The other institutes do not have publications pages on their
websites but I know some well published colleagues there except the Institute of Mathematics.
Item (4) above explains why the Institute has all the time to carry on this vilification campaign during
the last 23 years.
This candid look at the Institute is not washing dirty linen in public since the Institute’s website is
viewed worldwide. Rather, it poses a challenge for the College: What can be done to lift the only
Institute that rides on its prestige but failed to deliver?
If I had a glass roof over my head I would not push my luck but keep away from trouble.
(When this article was first published online the Institute website’s publications page closed down
with the sign, “Under Construction”.
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The Institute of Mathematics is at it Again
The Institute of Mathematics has posted its 4rth anonymous statement since 2005 (URL:
http://en.wikipilipinas.org/index.php?title=Edgar_Escultura) attacking me personally and my work based
on misinformation and ignorance of mathematics, physics and mathematical issues. The statement
must have been authorized by its Director, Dr. Jose Balmaceda, if he himself is not its author. At any
rate, he takes full responsibility for it as IM director. The message replaces an earlier one in this
website of WikiPilipinas that labelled as hoaxes the inventions and scientific discoveries of Agapito
Flores, Eduardo San Juan, Fe de Mundo and my scientific discoveries without any documentation
whatsoever. It was deleted and replaced by this 4rth IM statement only after I pointed out its libellous
nature. The 3rd anonymous IM statement has likewise been deleted as well as a fake apology linked
to this website.
The reason for the anonymity is quite obvious: Dr. Balmaceda is not a mathematician (i.e., he has no
publication in any of the peer reviewed international scientific or mathematical journals whatsoever)
but pretends to know mathematics by commenting on mathematical issues he does not understand
(e.g. he thinks peer review is done by bloggers, view URL:
http://en.wikipilipinas.org/index.php?title=Edgar_Escultura). Thus, he is, objectively, an impostor
and a discredit to the University of the Philippines where he occupies such a high position.
I could have ignored this message since it does not make a dent on my stature as a mathematician and
physicist of world renown based on my over fifty peer-reviewed scientific articles, books and keynote
addresses at international scientific conferences many of which monumental such as (1) the solution
of the 200-year-old gravitational n-body problem, (2) The development of the grand unified theory (a
project that Albert Einstein proposed over 70 years ago but failed to carry out), (3) disproof of the
360-year-old Fermat’s conjecture known as Fermat’s last theorem, (4) my proof of the 250-year-old
Goldbach’s conjecture (the proof is in my article, The new real number system and discrete
computation and calculus, Neural, Parallel and Scientific Computations, 2009, 17, pp. 59 – 84) and
my ebook, Scientific Natural Philosophy (my publications are listed on my website,
http://users.tpg.com.au/pidro/, under the article Abstracts and Summary of Publications) but I
responded to all challenges across cyberspace including those raised by the IM statements to share the
discussion with amateurs and mathematics and physics teachers. (This opens up a new era in
mathematics where mathematical and scientific results are discussed openly so that hoaxes can no
longer stand or errors hide for a long time). Not a single mathematician or physicist has ever refuted
my work.
The Nonsense of Dr. Jose Balmaceda
An excerpt from a webpage of WiikiPilipinas,
http://en.wikipilipinas.org/index.php?title=Edgar_Escultura,
says:
A Proof that d* = 0
Dr. Escultura defines his 'dark number' d* as d* = 1 - .9999999... (where .999999.... is a never ending
string of 9's after the decimal place). He also claims that d* > 0, so this 'dark number' is NOT zero
accordind to Escultura. So we will begin with two simple legal equations, then subtract the second
equation from the first and examine the result. So as not to confuse the * in (d*) with the
multiplication sign (*), in the following equations we will write D in place of d*, that is D = d* = (1 -
.999999...)
(1) 10*(D) = 10*(1 - .999999..) = 10 - 9.999999...
(2) 1*(D) = 1*(1 - .999999...) = 1 - .999999...
Now we subtract equation (2) from equation (1):
10*(D) - 1*(D) = (10 - 9.999999...) - (1 - .999999...)
= 10 - 9.999999... - 1 + .999999...
= (10 - 1) - (9.999999... - .999999...) = 9 - 9.000000... = 0
Also we have
10*(D) - 1*(D) = (10 - 1) * D = 9*D.
So now we have,
9*D = 0 (by equating the results of the above two equations)
D = 0/9 = D = 0
Thus we have proven that in fact if we accept this 'dark number' d*, then it must be the case that d* =
0. However, Escultura explicitly claims that d* > 0.
A Proof that .999999... = 1
It is possible that some people may not be comfortable with the fact that .999999.... = 1. It may seem
at first that .999999... is strictly less than 1, however this is a peculiarity of how we write out numbers,
and I assure you it is true. As above we will start with two perfectly legal equations and again subtract
one from the other to see where it leads.
(1) 10*(.999999...) = 9.999999...
(2) 1*(.999999...) = .999999...
Now we subtract equation (2) from equation (1)
10*(.999999...) - 1*(.999999...) = 9.999999... - .999999... = 9.000000...
Also we have,
10*(.999999...) - 1*(.999999...) = (10 - 1)*(.999999...) = 9*(.999999...).
So now we have,
9*(.999999...) = 9.000000... (by equating the results above two),
(.999999...) = (9.000000...)/9
.999999... = 9/9 (clearly 9.000000... = 9)
.999999... = 1
Thus .999999... may appear at first to be a number smaller that 1, it is in fact equal to 1. There is
nothing 'wrong' with this, it is just a quirk of the decimal system we use to write our numbers. This
allows us to quickly show that d* = 0, as in the following proof:
d* = (1 - .999999...) = (1 - 1) (since we now know that .999... = 1) = 0.
=======
Let me just comment on two of the many nonsense of these "proofs".
1) Proof of d* = 0.
The equation D = d* = (1 - .999999...) is ill -defined, nonsense, IN THE REAL NUMBER SYSTEM
because all nonterminating decimals including .99... is ill-defined there and do not belong to it (they
are well defined in the new real number system). Therefore, the equations,
(1) 10*(D) = 10*(1 - .999999..) = 10 - 9.999999...
(2) 1*(D) = 1*(1 - .999999...) = 1 - .999999...
are nonsense because they apply multiplication and subtraction, the inverse of the addition, which are
binary operations of the real number system, to numbers that do not belong to it. Consequently, the
whole "proof" is total nonsense.
In particular, one cannot apply addition and multiplication (as binary operations IN THE REAL
NUMBER SYSTEM) precisely because they are ill-defined in the real number system. Try, for
instance, adding sqrt2 and sqrt3 and I’ll bet my life that no one can do it. It can be approximated by
some real number but that is not the sum. However, it can be done in the new real number system
because nonterminating decimals are well defined.
2) A Proof that .999999... = 1
The comment in 1) applies as well to the equations,
(1) 10*(D) = 10*(1 - .999999..) = 10 - 9.999999...
(2) 1*(D) = 1*(1 - .999999...) = 1 - .999999...,
which combine a mix of elements NOT BELONGING TO THE REAL NUMBER SYSTEM in a set
of binary operations IN THE REAL NUMBER SYSTEM. Thus, the proof is also nonsense.
Such sloppy mathematics could not have come from a true mathematician. Both errors are quite basic
and reveal utter ignorance of the fundamentals of mathematics. This is a problem peculiar to amateurs
who know only mechanical manipulation of symbols but are ignorant of precise mathematical
reasoning and deep analysis. Moreover, it appears that Dr. Balmaceda is a new comer to internet
mathematics forums where I have posted many, many responses to hundreds of bloggers including my
responses to ALL the points being raised here..
I could have referred Dr. Balmaceda to my original work but, not being a mathematician, i.e., having
no publication in any peer reviewed international journal, he would neither understand my work nor
know such journals. He does not even know which journals are peer reviewed and who the
mathematicians are and that is understandable.
This tit-for-tat with me is an exercise in futility for Dr. Balmaceda, although it wastes my time, and
works to his disadvantage. For, it only reveals more and more (1) my achievements as a
mathematician and physicist of world renown and (2) his true status as an impostor parading as a
mathematician. Remember that there is a light year of difference between a mathematician and a
mathematics teacher.
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